Properties

Label 6010.2.a.c.1.13
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(1.84416\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+0.844163 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(+0.844163 q^{6}\) \(-0.532701 q^{7}\) \(+1.00000 q^{8}\) \(-2.28739 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+0.844163 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(+0.844163 q^{6}\) \(-0.532701 q^{7}\) \(+1.00000 q^{8}\) \(-2.28739 q^{9}\) \(+1.00000 q^{10}\) \(-0.961430 q^{11}\) \(+0.844163 q^{12}\) \(-1.20269 q^{13}\) \(-0.532701 q^{14}\) \(+0.844163 q^{15}\) \(+1.00000 q^{16}\) \(-5.49260 q^{17}\) \(-2.28739 q^{18}\) \(-4.34072 q^{19}\) \(+1.00000 q^{20}\) \(-0.449687 q^{21}\) \(-0.961430 q^{22}\) \(+6.60521 q^{23}\) \(+0.844163 q^{24}\) \(+1.00000 q^{25}\) \(-1.20269 q^{26}\) \(-4.46342 q^{27}\) \(-0.532701 q^{28}\) \(-7.33783 q^{29}\) \(+0.844163 q^{30}\) \(+7.02057 q^{31}\) \(+1.00000 q^{32}\) \(-0.811604 q^{33}\) \(-5.49260 q^{34}\) \(-0.532701 q^{35}\) \(-2.28739 q^{36}\) \(-5.84241 q^{37}\) \(-4.34072 q^{38}\) \(-1.01527 q^{39}\) \(+1.00000 q^{40}\) \(+9.20135 q^{41}\) \(-0.449687 q^{42}\) \(-9.44089 q^{43}\) \(-0.961430 q^{44}\) \(-2.28739 q^{45}\) \(+6.60521 q^{46}\) \(-7.28325 q^{47}\) \(+0.844163 q^{48}\) \(-6.71623 q^{49}\) \(+1.00000 q^{50}\) \(-4.63665 q^{51}\) \(-1.20269 q^{52}\) \(+6.24445 q^{53}\) \(-4.46342 q^{54}\) \(-0.961430 q^{55}\) \(-0.532701 q^{56}\) \(-3.66427 q^{57}\) \(-7.33783 q^{58}\) \(-9.77782 q^{59}\) \(+0.844163 q^{60}\) \(-5.61164 q^{61}\) \(+7.02057 q^{62}\) \(+1.21849 q^{63}\) \(+1.00000 q^{64}\) \(-1.20269 q^{65}\) \(-0.811604 q^{66}\) \(+11.5528 q^{67}\) \(-5.49260 q^{68}\) \(+5.57587 q^{69}\) \(-0.532701 q^{70}\) \(-3.84683 q^{71}\) \(-2.28739 q^{72}\) \(+7.54343 q^{73}\) \(-5.84241 q^{74}\) \(+0.844163 q^{75}\) \(-4.34072 q^{76}\) \(+0.512155 q^{77}\) \(-1.01527 q^{78}\) \(-0.0908517 q^{79}\) \(+1.00000 q^{80}\) \(+3.09431 q^{81}\) \(+9.20135 q^{82}\) \(-13.2425 q^{83}\) \(-0.449687 q^{84}\) \(-5.49260 q^{85}\) \(-9.44089 q^{86}\) \(-6.19432 q^{87}\) \(-0.961430 q^{88}\) \(-14.0969 q^{89}\) \(-2.28739 q^{90}\) \(+0.640674 q^{91}\) \(+6.60521 q^{92}\) \(+5.92651 q^{93}\) \(-7.28325 q^{94}\) \(-4.34072 q^{95}\) \(+0.844163 q^{96}\) \(+8.35252 q^{97}\) \(-6.71623 q^{98}\) \(+2.19917 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 27q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 17q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 11q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 16q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut -\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 17q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 35q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 11q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut -\mathstrut 6q^{57} \) \(\mathstrut -\mathstrut 23q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 21q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut -\mathstrut 25q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 17q^{76} \) \(\mathstrut -\mathstrut 34q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 35q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut +\mathstrut 3q^{86} \) \(\mathstrut +\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut -\mathstrut 9q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut -\mathstrut 25q^{94} \) \(\mathstrut -\mathstrut 17q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 21q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.844163 0.487378 0.243689 0.969853i \(-0.421642\pi\)
0.243689 + 0.969853i \(0.421642\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 0.844163 0.344628
\(7\) −0.532701 −0.201342 −0.100671 0.994920i \(-0.532099\pi\)
−0.100671 + 0.994920i \(0.532099\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.28739 −0.762463
\(10\) 1.00000 0.316228
\(11\) −0.961430 −0.289882 −0.144941 0.989440i \(-0.546299\pi\)
−0.144941 + 0.989440i \(0.546299\pi\)
\(12\) 0.844163 0.243689
\(13\) −1.20269 −0.333566 −0.166783 0.985994i \(-0.553338\pi\)
−0.166783 + 0.985994i \(0.553338\pi\)
\(14\) −0.532701 −0.142370
\(15\) 0.844163 0.217962
\(16\) 1.00000 0.250000
\(17\) −5.49260 −1.33215 −0.666076 0.745884i \(-0.732027\pi\)
−0.666076 + 0.745884i \(0.732027\pi\)
\(18\) −2.28739 −0.539143
\(19\) −4.34072 −0.995829 −0.497914 0.867226i \(-0.665901\pi\)
−0.497914 + 0.867226i \(0.665901\pi\)
\(20\) 1.00000 0.223607
\(21\) −0.449687 −0.0981297
\(22\) −0.961430 −0.204978
\(23\) 6.60521 1.37728 0.688641 0.725103i \(-0.258208\pi\)
0.688641 + 0.725103i \(0.258208\pi\)
\(24\) 0.844163 0.172314
\(25\) 1.00000 0.200000
\(26\) −1.20269 −0.235867
\(27\) −4.46342 −0.858985
\(28\) −0.532701 −0.100671
\(29\) −7.33783 −1.36260 −0.681300 0.732004i \(-0.738585\pi\)
−0.681300 + 0.732004i \(0.738585\pi\)
\(30\) 0.844163 0.154122
\(31\) 7.02057 1.26093 0.630466 0.776217i \(-0.282864\pi\)
0.630466 + 0.776217i \(0.282864\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.811604 −0.141282
\(34\) −5.49260 −0.941974
\(35\) −0.532701 −0.0900429
\(36\) −2.28739 −0.381231
\(37\) −5.84241 −0.960486 −0.480243 0.877136i \(-0.659451\pi\)
−0.480243 + 0.877136i \(0.659451\pi\)
\(38\) −4.34072 −0.704157
\(39\) −1.01527 −0.162573
\(40\) 1.00000 0.158114
\(41\) 9.20135 1.43701 0.718504 0.695522i \(-0.244827\pi\)
0.718504 + 0.695522i \(0.244827\pi\)
\(42\) −0.449687 −0.0693881
\(43\) −9.44089 −1.43972 −0.719861 0.694118i \(-0.755795\pi\)
−0.719861 + 0.694118i \(0.755795\pi\)
\(44\) −0.961430 −0.144941
\(45\) −2.28739 −0.340984
\(46\) 6.60521 0.973885
\(47\) −7.28325 −1.06237 −0.531186 0.847255i \(-0.678253\pi\)
−0.531186 + 0.847255i \(0.678253\pi\)
\(48\) 0.844163 0.121844
\(49\) −6.71623 −0.959461
\(50\) 1.00000 0.141421
\(51\) −4.63665 −0.649261
\(52\) −1.20269 −0.166783
\(53\) 6.24445 0.857742 0.428871 0.903366i \(-0.358912\pi\)
0.428871 + 0.903366i \(0.358912\pi\)
\(54\) −4.46342 −0.607394
\(55\) −0.961430 −0.129639
\(56\) −0.532701 −0.0711852
\(57\) −3.66427 −0.485345
\(58\) −7.33783 −0.963504
\(59\) −9.77782 −1.27296 −0.636482 0.771292i \(-0.719611\pi\)
−0.636482 + 0.771292i \(0.719611\pi\)
\(60\) 0.844163 0.108981
\(61\) −5.61164 −0.718497 −0.359249 0.933242i \(-0.616967\pi\)
−0.359249 + 0.933242i \(0.616967\pi\)
\(62\) 7.02057 0.891614
\(63\) 1.21849 0.153516
\(64\) 1.00000 0.125000
\(65\) −1.20269 −0.149175
\(66\) −0.811604 −0.0999015
\(67\) 11.5528 1.41140 0.705700 0.708511i \(-0.250633\pi\)
0.705700 + 0.708511i \(0.250633\pi\)
\(68\) −5.49260 −0.666076
\(69\) 5.57587 0.671256
\(70\) −0.532701 −0.0636700
\(71\) −3.84683 −0.456534 −0.228267 0.973599i \(-0.573306\pi\)
−0.228267 + 0.973599i \(0.573306\pi\)
\(72\) −2.28739 −0.269571
\(73\) 7.54343 0.882891 0.441446 0.897288i \(-0.354466\pi\)
0.441446 + 0.897288i \(0.354466\pi\)
\(74\) −5.84241 −0.679166
\(75\) 0.844163 0.0974755
\(76\) −4.34072 −0.497914
\(77\) 0.512155 0.0583655
\(78\) −1.01527 −0.114956
\(79\) −0.0908517 −0.0102216 −0.00511081 0.999987i \(-0.501627\pi\)
−0.00511081 + 0.999987i \(0.501627\pi\)
\(80\) 1.00000 0.111803
\(81\) 3.09431 0.343813
\(82\) 9.20135 1.01612
\(83\) −13.2425 −1.45355 −0.726775 0.686876i \(-0.758982\pi\)
−0.726775 + 0.686876i \(0.758982\pi\)
\(84\) −0.449687 −0.0490648
\(85\) −5.49260 −0.595756
\(86\) −9.44089 −1.01804
\(87\) −6.19432 −0.664101
\(88\) −0.961430 −0.102489
\(89\) −14.0969 −1.49426 −0.747132 0.664675i \(-0.768570\pi\)
−0.747132 + 0.664675i \(0.768570\pi\)
\(90\) −2.28739 −0.241112
\(91\) 0.640674 0.0671609
\(92\) 6.60521 0.688641
\(93\) 5.92651 0.614550
\(94\) −7.28325 −0.751210
\(95\) −4.34072 −0.445348
\(96\) 0.844163 0.0861570
\(97\) 8.35252 0.848070 0.424035 0.905646i \(-0.360613\pi\)
0.424035 + 0.905646i \(0.360613\pi\)
\(98\) −6.71623 −0.678442
\(99\) 2.19917 0.221024
\(100\) 1.00000 0.100000
\(101\) 9.85205 0.980315 0.490158 0.871634i \(-0.336939\pi\)
0.490158 + 0.871634i \(0.336939\pi\)
\(102\) −4.63665 −0.459097
\(103\) −15.3763 −1.51507 −0.757534 0.652795i \(-0.773596\pi\)
−0.757534 + 0.652795i \(0.773596\pi\)
\(104\) −1.20269 −0.117933
\(105\) −0.449687 −0.0438849
\(106\) 6.24445 0.606515
\(107\) −4.15714 −0.401886 −0.200943 0.979603i \(-0.564401\pi\)
−0.200943 + 0.979603i \(0.564401\pi\)
\(108\) −4.46342 −0.429493
\(109\) −0.609510 −0.0583805 −0.0291902 0.999574i \(-0.509293\pi\)
−0.0291902 + 0.999574i \(0.509293\pi\)
\(110\) −0.961430 −0.0916688
\(111\) −4.93194 −0.468119
\(112\) −0.532701 −0.0503355
\(113\) −5.36554 −0.504748 −0.252374 0.967630i \(-0.581211\pi\)
−0.252374 + 0.967630i \(0.581211\pi\)
\(114\) −3.66427 −0.343191
\(115\) 6.60521 0.615939
\(116\) −7.33783 −0.681300
\(117\) 2.75102 0.254332
\(118\) −9.77782 −0.900121
\(119\) 2.92592 0.268218
\(120\) 0.844163 0.0770612
\(121\) −10.0757 −0.915968
\(122\) −5.61164 −0.508054
\(123\) 7.76744 0.700366
\(124\) 7.02057 0.630466
\(125\) 1.00000 0.0894427
\(126\) 1.21849 0.108552
\(127\) −5.62604 −0.499231 −0.249615 0.968345i \(-0.580304\pi\)
−0.249615 + 0.968345i \(0.580304\pi\)
\(128\) 1.00000 0.0883883
\(129\) −7.96965 −0.701689
\(130\) −1.20269 −0.105483
\(131\) 0.518832 0.0453306 0.0226653 0.999743i \(-0.492785\pi\)
0.0226653 + 0.999743i \(0.492785\pi\)
\(132\) −0.811604 −0.0706411
\(133\) 2.31231 0.200502
\(134\) 11.5528 0.998011
\(135\) −4.46342 −0.384150
\(136\) −5.49260 −0.470987
\(137\) −4.41924 −0.377561 −0.188780 0.982019i \(-0.560453\pi\)
−0.188780 + 0.982019i \(0.560453\pi\)
\(138\) 5.57587 0.474650
\(139\) −22.4968 −1.90815 −0.954076 0.299563i \(-0.903159\pi\)
−0.954076 + 0.299563i \(0.903159\pi\)
\(140\) −0.532701 −0.0450215
\(141\) −6.14825 −0.517776
\(142\) −3.84683 −0.322819
\(143\) 1.15630 0.0966948
\(144\) −2.28739 −0.190616
\(145\) −7.33783 −0.609373
\(146\) 7.54343 0.624298
\(147\) −5.66959 −0.467620
\(148\) −5.84241 −0.480243
\(149\) 19.7775 1.62023 0.810117 0.586268i \(-0.199403\pi\)
0.810117 + 0.586268i \(0.199403\pi\)
\(150\) 0.844163 0.0689256
\(151\) −6.89037 −0.560730 −0.280365 0.959893i \(-0.590456\pi\)
−0.280365 + 0.959893i \(0.590456\pi\)
\(152\) −4.34072 −0.352079
\(153\) 12.5637 1.01572
\(154\) 0.512155 0.0412706
\(155\) 7.02057 0.563906
\(156\) −1.01527 −0.0812863
\(157\) −6.83852 −0.545774 −0.272887 0.962046i \(-0.587978\pi\)
−0.272887 + 0.962046i \(0.587978\pi\)
\(158\) −0.0908517 −0.00722777
\(159\) 5.27134 0.418044
\(160\) 1.00000 0.0790569
\(161\) −3.51860 −0.277305
\(162\) 3.09431 0.243112
\(163\) −2.76885 −0.216873 −0.108437 0.994103i \(-0.534584\pi\)
−0.108437 + 0.994103i \(0.534584\pi\)
\(164\) 9.20135 0.718504
\(165\) −0.811604 −0.0631833
\(166\) −13.2425 −1.02782
\(167\) −4.26084 −0.329714 −0.164857 0.986317i \(-0.552716\pi\)
−0.164857 + 0.986317i \(0.552716\pi\)
\(168\) −0.449687 −0.0346941
\(169\) −11.5535 −0.888734
\(170\) −5.49260 −0.421263
\(171\) 9.92891 0.759283
\(172\) −9.44089 −0.719861
\(173\) 8.79251 0.668482 0.334241 0.942488i \(-0.391520\pi\)
0.334241 + 0.942488i \(0.391520\pi\)
\(174\) −6.19432 −0.469590
\(175\) −0.532701 −0.0402684
\(176\) −0.961430 −0.0724705
\(177\) −8.25407 −0.620414
\(178\) −14.0969 −1.05660
\(179\) 11.7877 0.881051 0.440525 0.897740i \(-0.354792\pi\)
0.440525 + 0.897740i \(0.354792\pi\)
\(180\) −2.28739 −0.170492
\(181\) 24.3416 1.80930 0.904648 0.426159i \(-0.140133\pi\)
0.904648 + 0.426159i \(0.140133\pi\)
\(182\) 0.640674 0.0474899
\(183\) −4.73714 −0.350180
\(184\) 6.60521 0.486942
\(185\) −5.84241 −0.429542
\(186\) 5.92651 0.434553
\(187\) 5.28076 0.386167
\(188\) −7.28325 −0.531186
\(189\) 2.37767 0.172950
\(190\) −4.34072 −0.314909
\(191\) 12.8086 0.926796 0.463398 0.886150i \(-0.346630\pi\)
0.463398 + 0.886150i \(0.346630\pi\)
\(192\) 0.844163 0.0609222
\(193\) 20.6520 1.48657 0.743283 0.668978i \(-0.233268\pi\)
0.743283 + 0.668978i \(0.233268\pi\)
\(194\) 8.35252 0.599676
\(195\) −1.01527 −0.0727047
\(196\) −6.71623 −0.479731
\(197\) −12.6133 −0.898659 −0.449329 0.893366i \(-0.648337\pi\)
−0.449329 + 0.893366i \(0.648337\pi\)
\(198\) 2.19917 0.156288
\(199\) 22.9659 1.62801 0.814005 0.580858i \(-0.197283\pi\)
0.814005 + 0.580858i \(0.197283\pi\)
\(200\) 1.00000 0.0707107
\(201\) 9.75245 0.687885
\(202\) 9.85205 0.693188
\(203\) 3.90887 0.274349
\(204\) −4.63665 −0.324631
\(205\) 9.20135 0.642650
\(206\) −15.3763 −1.07132
\(207\) −15.1087 −1.05013
\(208\) −1.20269 −0.0833915
\(209\) 4.17330 0.288673
\(210\) −0.449687 −0.0310313
\(211\) −20.3893 −1.40366 −0.701830 0.712344i \(-0.747633\pi\)
−0.701830 + 0.712344i \(0.747633\pi\)
\(212\) 6.24445 0.428871
\(213\) −3.24735 −0.222505
\(214\) −4.15714 −0.284176
\(215\) −9.44089 −0.643863
\(216\) −4.46342 −0.303697
\(217\) −3.73987 −0.253879
\(218\) −0.609510 −0.0412812
\(219\) 6.36788 0.430302
\(220\) −0.961430 −0.0648196
\(221\) 6.60589 0.444360
\(222\) −4.93194 −0.331010
\(223\) −18.2859 −1.22452 −0.612258 0.790658i \(-0.709739\pi\)
−0.612258 + 0.790658i \(0.709739\pi\)
\(224\) −0.532701 −0.0355926
\(225\) −2.28739 −0.152493
\(226\) −5.36554 −0.356911
\(227\) 23.9381 1.58883 0.794414 0.607376i \(-0.207778\pi\)
0.794414 + 0.607376i \(0.207778\pi\)
\(228\) −3.66427 −0.242672
\(229\) 23.1069 1.52695 0.763473 0.645840i \(-0.223493\pi\)
0.763473 + 0.645840i \(0.223493\pi\)
\(230\) 6.60521 0.435534
\(231\) 0.432342 0.0284460
\(232\) −7.33783 −0.481752
\(233\) 10.5496 0.691125 0.345562 0.938396i \(-0.387688\pi\)
0.345562 + 0.938396i \(0.387688\pi\)
\(234\) 2.75102 0.179840
\(235\) −7.28325 −0.475107
\(236\) −9.77782 −0.636482
\(237\) −0.0766937 −0.00498179
\(238\) 2.92592 0.189659
\(239\) 2.97603 0.192503 0.0962515 0.995357i \(-0.469315\pi\)
0.0962515 + 0.995357i \(0.469315\pi\)
\(240\) 0.844163 0.0544905
\(241\) −22.2492 −1.43320 −0.716600 0.697484i \(-0.754303\pi\)
−0.716600 + 0.697484i \(0.754303\pi\)
\(242\) −10.0757 −0.647687
\(243\) 16.0024 1.02655
\(244\) −5.61164 −0.359249
\(245\) −6.71623 −0.429084
\(246\) 7.76744 0.495234
\(247\) 5.22053 0.332175
\(248\) 7.02057 0.445807
\(249\) −11.1788 −0.708428
\(250\) 1.00000 0.0632456
\(251\) −12.4001 −0.782689 −0.391344 0.920244i \(-0.627990\pi\)
−0.391344 + 0.920244i \(0.627990\pi\)
\(252\) 1.21849 0.0767579
\(253\) −6.35045 −0.399249
\(254\) −5.62604 −0.353009
\(255\) −4.63665 −0.290358
\(256\) 1.00000 0.0625000
\(257\) −2.07976 −0.129732 −0.0648659 0.997894i \(-0.520662\pi\)
−0.0648659 + 0.997894i \(0.520662\pi\)
\(258\) −7.96965 −0.496169
\(259\) 3.11226 0.193386
\(260\) −1.20269 −0.0745876
\(261\) 16.7845 1.03893
\(262\) 0.518832 0.0320536
\(263\) 4.98966 0.307675 0.153838 0.988096i \(-0.450837\pi\)
0.153838 + 0.988096i \(0.450837\pi\)
\(264\) −0.811604 −0.0499508
\(265\) 6.24445 0.383594
\(266\) 2.31231 0.141777
\(267\) −11.9001 −0.728271
\(268\) 11.5528 0.705700
\(269\) 0.908252 0.0553771 0.0276886 0.999617i \(-0.491185\pi\)
0.0276886 + 0.999617i \(0.491185\pi\)
\(270\) −4.46342 −0.271635
\(271\) 16.6795 1.01321 0.506603 0.862180i \(-0.330901\pi\)
0.506603 + 0.862180i \(0.330901\pi\)
\(272\) −5.49260 −0.333038
\(273\) 0.540833 0.0327327
\(274\) −4.41924 −0.266976
\(275\) −0.961430 −0.0579764
\(276\) 5.57587 0.335628
\(277\) 27.1449 1.63098 0.815489 0.578772i \(-0.196468\pi\)
0.815489 + 0.578772i \(0.196468\pi\)
\(278\) −22.4968 −1.34927
\(279\) −16.0588 −0.961414
\(280\) −0.532701 −0.0318350
\(281\) −15.7002 −0.936595 −0.468297 0.883571i \(-0.655132\pi\)
−0.468297 + 0.883571i \(0.655132\pi\)
\(282\) −6.14825 −0.366123
\(283\) 17.5279 1.04192 0.520962 0.853580i \(-0.325573\pi\)
0.520962 + 0.853580i \(0.325573\pi\)
\(284\) −3.84683 −0.228267
\(285\) −3.66427 −0.217053
\(286\) 1.15630 0.0683736
\(287\) −4.90157 −0.289330
\(288\) −2.28739 −0.134786
\(289\) 13.1687 0.774628
\(290\) −7.33783 −0.430892
\(291\) 7.05089 0.413330
\(292\) 7.54343 0.441446
\(293\) −27.7763 −1.62271 −0.811355 0.584553i \(-0.801270\pi\)
−0.811355 + 0.584553i \(0.801270\pi\)
\(294\) −5.66959 −0.330657
\(295\) −9.77782 −0.569287
\(296\) −5.84241 −0.339583
\(297\) 4.29127 0.249005
\(298\) 19.7775 1.14568
\(299\) −7.94401 −0.459414
\(300\) 0.844163 0.0487378
\(301\) 5.02917 0.289877
\(302\) −6.89037 −0.396496
\(303\) 8.31673 0.477784
\(304\) −4.34072 −0.248957
\(305\) −5.61164 −0.321322
\(306\) 12.5637 0.718220
\(307\) 30.2322 1.72545 0.862723 0.505677i \(-0.168757\pi\)
0.862723 + 0.505677i \(0.168757\pi\)
\(308\) 0.512155 0.0291827
\(309\) −12.9801 −0.738411
\(310\) 7.02057 0.398742
\(311\) 12.3450 0.700021 0.350011 0.936746i \(-0.386178\pi\)
0.350011 + 0.936746i \(0.386178\pi\)
\(312\) −1.01527 −0.0574781
\(313\) −31.9710 −1.80711 −0.903554 0.428474i \(-0.859051\pi\)
−0.903554 + 0.428474i \(0.859051\pi\)
\(314\) −6.83852 −0.385920
\(315\) 1.21849 0.0686544
\(316\) −0.0908517 −0.00511081
\(317\) −8.44300 −0.474206 −0.237103 0.971485i \(-0.576198\pi\)
−0.237103 + 0.971485i \(0.576198\pi\)
\(318\) 5.27134 0.295602
\(319\) 7.05481 0.394993
\(320\) 1.00000 0.0559017
\(321\) −3.50930 −0.195870
\(322\) −3.51860 −0.196084
\(323\) 23.8418 1.32660
\(324\) 3.09431 0.171906
\(325\) −1.20269 −0.0667132
\(326\) −2.76885 −0.153352
\(327\) −0.514526 −0.0284533
\(328\) 9.20135 0.508059
\(329\) 3.87980 0.213900
\(330\) −0.811604 −0.0446773
\(331\) 16.6072 0.912815 0.456408 0.889771i \(-0.349136\pi\)
0.456408 + 0.889771i \(0.349136\pi\)
\(332\) −13.2425 −0.726775
\(333\) 13.3639 0.732335
\(334\) −4.26084 −0.233143
\(335\) 11.5528 0.631197
\(336\) −0.449687 −0.0245324
\(337\) −14.1086 −0.768543 −0.384272 0.923220i \(-0.625547\pi\)
−0.384272 + 0.923220i \(0.625547\pi\)
\(338\) −11.5535 −0.628430
\(339\) −4.52939 −0.246003
\(340\) −5.49260 −0.297878
\(341\) −6.74979 −0.365522
\(342\) 9.92891 0.536894
\(343\) 7.30665 0.394522
\(344\) −9.44089 −0.509019
\(345\) 5.57587 0.300195
\(346\) 8.79251 0.472688
\(347\) −33.9642 −1.82329 −0.911647 0.410975i \(-0.865188\pi\)
−0.911647 + 0.410975i \(0.865188\pi\)
\(348\) −6.19432 −0.332050
\(349\) 13.0855 0.700453 0.350227 0.936665i \(-0.386105\pi\)
0.350227 + 0.936665i \(0.386105\pi\)
\(350\) −0.532701 −0.0284741
\(351\) 5.36810 0.286528
\(352\) −0.961430 −0.0512444
\(353\) −16.0428 −0.853873 −0.426936 0.904282i \(-0.640407\pi\)
−0.426936 + 0.904282i \(0.640407\pi\)
\(354\) −8.25407 −0.438699
\(355\) −3.84683 −0.204168
\(356\) −14.0969 −0.747132
\(357\) 2.46995 0.130724
\(358\) 11.7877 0.622997
\(359\) 0.802407 0.0423494 0.0211747 0.999776i \(-0.493259\pi\)
0.0211747 + 0.999776i \(0.493259\pi\)
\(360\) −2.28739 −0.120556
\(361\) −0.158171 −0.00832478
\(362\) 24.3416 1.27937
\(363\) −8.50549 −0.446423
\(364\) 0.640674 0.0335804
\(365\) 7.54343 0.394841
\(366\) −4.73714 −0.247614
\(367\) 7.01696 0.366282 0.183141 0.983087i \(-0.441373\pi\)
0.183141 + 0.983087i \(0.441373\pi\)
\(368\) 6.60521 0.344320
\(369\) −21.0471 −1.09567
\(370\) −5.84241 −0.303732
\(371\) −3.32643 −0.172700
\(372\) 5.92651 0.307275
\(373\) 14.4241 0.746854 0.373427 0.927660i \(-0.378183\pi\)
0.373427 + 0.927660i \(0.378183\pi\)
\(374\) 5.28076 0.273061
\(375\) 0.844163 0.0435924
\(376\) −7.28325 −0.375605
\(377\) 8.82512 0.454517
\(378\) 2.37767 0.122294
\(379\) −0.642511 −0.0330036 −0.0165018 0.999864i \(-0.505253\pi\)
−0.0165018 + 0.999864i \(0.505253\pi\)
\(380\) −4.34072 −0.222674
\(381\) −4.74930 −0.243314
\(382\) 12.8086 0.655344
\(383\) −8.96481 −0.458080 −0.229040 0.973417i \(-0.573559\pi\)
−0.229040 + 0.973417i \(0.573559\pi\)
\(384\) 0.844163 0.0430785
\(385\) 0.512155 0.0261018
\(386\) 20.6520 1.05116
\(387\) 21.5950 1.09773
\(388\) 8.35252 0.424035
\(389\) 37.1210 1.88211 0.941054 0.338257i \(-0.109837\pi\)
0.941054 + 0.338257i \(0.109837\pi\)
\(390\) −1.01527 −0.0514100
\(391\) −36.2798 −1.83475
\(392\) −6.71623 −0.339221
\(393\) 0.437979 0.0220931
\(394\) −12.6133 −0.635448
\(395\) −0.0908517 −0.00457125
\(396\) 2.19917 0.110512
\(397\) −19.5965 −0.983522 −0.491761 0.870730i \(-0.663647\pi\)
−0.491761 + 0.870730i \(0.663647\pi\)
\(398\) 22.9659 1.15118
\(399\) 1.95196 0.0977203
\(400\) 1.00000 0.0500000
\(401\) −15.5264 −0.775351 −0.387676 0.921796i \(-0.626722\pi\)
−0.387676 + 0.921796i \(0.626722\pi\)
\(402\) 9.75245 0.486408
\(403\) −8.44357 −0.420604
\(404\) 9.85205 0.490158
\(405\) 3.09431 0.153758
\(406\) 3.90887 0.193994
\(407\) 5.61707 0.278428
\(408\) −4.63665 −0.229548
\(409\) −24.6582 −1.21927 −0.609636 0.792682i \(-0.708684\pi\)
−0.609636 + 0.792682i \(0.708684\pi\)
\(410\) 9.20135 0.454422
\(411\) −3.73056 −0.184015
\(412\) −15.3763 −0.757534
\(413\) 5.20866 0.256301
\(414\) −15.1087 −0.742551
\(415\) −13.2425 −0.650047
\(416\) −1.20269 −0.0589667
\(417\) −18.9910 −0.929991
\(418\) 4.17330 0.204123
\(419\) −17.9818 −0.878470 −0.439235 0.898372i \(-0.644750\pi\)
−0.439235 + 0.898372i \(0.644750\pi\)
\(420\) −0.449687 −0.0219425
\(421\) 0.752344 0.0366670 0.0183335 0.999832i \(-0.494164\pi\)
0.0183335 + 0.999832i \(0.494164\pi\)
\(422\) −20.3893 −0.992538
\(423\) 16.6596 0.810019
\(424\) 6.24445 0.303258
\(425\) −5.49260 −0.266430
\(426\) −3.24735 −0.157335
\(427\) 2.98933 0.144664
\(428\) −4.15714 −0.200943
\(429\) 0.976107 0.0471269
\(430\) −9.44089 −0.455280
\(431\) 20.3211 0.978832 0.489416 0.872050i \(-0.337210\pi\)
0.489416 + 0.872050i \(0.337210\pi\)
\(432\) −4.46342 −0.214746
\(433\) −33.7894 −1.62381 −0.811907 0.583787i \(-0.801570\pi\)
−0.811907 + 0.583787i \(0.801570\pi\)
\(434\) −3.73987 −0.179519
\(435\) −6.19432 −0.296995
\(436\) −0.609510 −0.0291902
\(437\) −28.6713 −1.37154
\(438\) 6.36788 0.304269
\(439\) −22.3552 −1.06696 −0.533478 0.845814i \(-0.679115\pi\)
−0.533478 + 0.845814i \(0.679115\pi\)
\(440\) −0.961430 −0.0458344
\(441\) 15.3626 0.731554
\(442\) 6.60589 0.314210
\(443\) 21.2089 1.00766 0.503832 0.863802i \(-0.331923\pi\)
0.503832 + 0.863802i \(0.331923\pi\)
\(444\) −4.93194 −0.234060
\(445\) −14.0969 −0.668256
\(446\) −18.2859 −0.865863
\(447\) 16.6954 0.789666
\(448\) −0.532701 −0.0251678
\(449\) −24.8674 −1.17356 −0.586782 0.809745i \(-0.699606\pi\)
−0.586782 + 0.809745i \(0.699606\pi\)
\(450\) −2.28739 −0.107829
\(451\) −8.84645 −0.416563
\(452\) −5.36554 −0.252374
\(453\) −5.81659 −0.273287
\(454\) 23.9381 1.12347
\(455\) 0.640674 0.0300352
\(456\) −3.66427 −0.171595
\(457\) 38.5370 1.80268 0.901342 0.433109i \(-0.142583\pi\)
0.901342 + 0.433109i \(0.142583\pi\)
\(458\) 23.1069 1.07971
\(459\) 24.5158 1.14430
\(460\) 6.60521 0.307969
\(461\) 14.0184 0.652903 0.326451 0.945214i \(-0.394147\pi\)
0.326451 + 0.945214i \(0.394147\pi\)
\(462\) 0.432342 0.0201144
\(463\) 33.7519 1.56858 0.784291 0.620393i \(-0.213027\pi\)
0.784291 + 0.620393i \(0.213027\pi\)
\(464\) −7.33783 −0.340650
\(465\) 5.92651 0.274835
\(466\) 10.5496 0.488699
\(467\) 37.4995 1.73527 0.867635 0.497201i \(-0.165639\pi\)
0.867635 + 0.497201i \(0.165639\pi\)
\(468\) 2.75102 0.127166
\(469\) −6.15419 −0.284174
\(470\) −7.28325 −0.335951
\(471\) −5.77283 −0.265998
\(472\) −9.77782 −0.450061
\(473\) 9.07676 0.417350
\(474\) −0.0766937 −0.00352266
\(475\) −4.34072 −0.199166
\(476\) 2.92592 0.134109
\(477\) −14.2835 −0.653996
\(478\) 2.97603 0.136120
\(479\) −31.2817 −1.42930 −0.714648 0.699484i \(-0.753413\pi\)
−0.714648 + 0.699484i \(0.753413\pi\)
\(480\) 0.844163 0.0385306
\(481\) 7.02660 0.320385
\(482\) −22.2492 −1.01343
\(483\) −2.97027 −0.135152
\(484\) −10.0757 −0.457984
\(485\) 8.35252 0.379268
\(486\) 16.0024 0.725882
\(487\) 9.32490 0.422552 0.211276 0.977426i \(-0.432238\pi\)
0.211276 + 0.977426i \(0.432238\pi\)
\(488\) −5.61164 −0.254027
\(489\) −2.33736 −0.105699
\(490\) −6.71623 −0.303408
\(491\) 34.9844 1.57882 0.789412 0.613863i \(-0.210385\pi\)
0.789412 + 0.613863i \(0.210385\pi\)
\(492\) 7.76744 0.350183
\(493\) 40.3038 1.81519
\(494\) 5.22053 0.234883
\(495\) 2.19917 0.0988451
\(496\) 7.02057 0.315233
\(497\) 2.04921 0.0919196
\(498\) −11.1788 −0.500934
\(499\) −37.5728 −1.68199 −0.840995 0.541043i \(-0.818030\pi\)
−0.840995 + 0.541043i \(0.818030\pi\)
\(500\) 1.00000 0.0447214
\(501\) −3.59685 −0.160695
\(502\) −12.4001 −0.553445
\(503\) 19.0226 0.848176 0.424088 0.905621i \(-0.360595\pi\)
0.424088 + 0.905621i \(0.360595\pi\)
\(504\) 1.21849 0.0542761
\(505\) 9.85205 0.438410
\(506\) −6.35045 −0.282312
\(507\) −9.75307 −0.433149
\(508\) −5.62604 −0.249615
\(509\) 28.1930 1.24963 0.624816 0.780772i \(-0.285174\pi\)
0.624816 + 0.780772i \(0.285174\pi\)
\(510\) −4.63665 −0.205314
\(511\) −4.01839 −0.177763
\(512\) 1.00000 0.0441942
\(513\) 19.3744 0.855402
\(514\) −2.07976 −0.0917342
\(515\) −15.3763 −0.677559
\(516\) −7.96965 −0.350844
\(517\) 7.00234 0.307963
\(518\) 3.11226 0.136745
\(519\) 7.42231 0.325803
\(520\) −1.20269 −0.0527414
\(521\) −13.1659 −0.576808 −0.288404 0.957509i \(-0.593125\pi\)
−0.288404 + 0.957509i \(0.593125\pi\)
\(522\) 16.7845 0.734636
\(523\) 16.5833 0.725136 0.362568 0.931957i \(-0.381900\pi\)
0.362568 + 0.931957i \(0.381900\pi\)
\(524\) 0.518832 0.0226653
\(525\) −0.449687 −0.0196259
\(526\) 4.98966 0.217559
\(527\) −38.5612 −1.67975
\(528\) −0.811604 −0.0353205
\(529\) 20.6288 0.896903
\(530\) 6.24445 0.271242
\(531\) 22.3657 0.970588
\(532\) 2.31231 0.100251
\(533\) −11.0664 −0.479337
\(534\) −11.9001 −0.514966
\(535\) −4.15714 −0.179729
\(536\) 11.5528 0.499005
\(537\) 9.95070 0.429404
\(538\) 0.908252 0.0391575
\(539\) 6.45719 0.278131
\(540\) −4.46342 −0.192075
\(541\) −5.59725 −0.240644 −0.120322 0.992735i \(-0.538393\pi\)
−0.120322 + 0.992735i \(0.538393\pi\)
\(542\) 16.6795 0.716445
\(543\) 20.5483 0.881811
\(544\) −5.49260 −0.235493
\(545\) −0.609510 −0.0261085
\(546\) 0.540833 0.0231455
\(547\) 30.5086 1.30445 0.652227 0.758024i \(-0.273835\pi\)
0.652227 + 0.758024i \(0.273835\pi\)
\(548\) −4.41924 −0.188780
\(549\) 12.8360 0.547827
\(550\) −0.961430 −0.0409955
\(551\) 31.8514 1.35692
\(552\) 5.57587 0.237325
\(553\) 0.0483968 0.00205804
\(554\) 27.1449 1.15328
\(555\) −4.93194 −0.209349
\(556\) −22.4968 −0.954076
\(557\) −15.7133 −0.665793 −0.332896 0.942963i \(-0.608026\pi\)
−0.332896 + 0.942963i \(0.608026\pi\)
\(558\) −16.0588 −0.679822
\(559\) 11.3545 0.480242
\(560\) −0.532701 −0.0225107
\(561\) 4.45782 0.188209
\(562\) −15.7002 −0.662273
\(563\) −31.9893 −1.34819 −0.674093 0.738646i \(-0.735465\pi\)
−0.674093 + 0.738646i \(0.735465\pi\)
\(564\) −6.14825 −0.258888
\(565\) −5.36554 −0.225730
\(566\) 17.5279 0.736751
\(567\) −1.64834 −0.0692240
\(568\) −3.84683 −0.161409
\(569\) −18.2157 −0.763643 −0.381821 0.924236i \(-0.624703\pi\)
−0.381821 + 0.924236i \(0.624703\pi\)
\(570\) −3.66427 −0.153480
\(571\) 28.0809 1.17515 0.587575 0.809170i \(-0.300083\pi\)
0.587575 + 0.809170i \(0.300083\pi\)
\(572\) 1.15630 0.0483474
\(573\) 10.8125 0.451700
\(574\) −4.90157 −0.204587
\(575\) 6.60521 0.275456
\(576\) −2.28739 −0.0953079
\(577\) −16.4558 −0.685062 −0.342531 0.939506i \(-0.611284\pi\)
−0.342531 + 0.939506i \(0.611284\pi\)
\(578\) 13.1687 0.547745
\(579\) 17.4337 0.724519
\(580\) −7.33783 −0.304687
\(581\) 7.05428 0.292661
\(582\) 7.05089 0.292269
\(583\) −6.00361 −0.248644
\(584\) 7.54343 0.312149
\(585\) 2.75102 0.113741
\(586\) −27.7763 −1.14743
\(587\) −2.02510 −0.0835848 −0.0417924 0.999126i \(-0.513307\pi\)
−0.0417924 + 0.999126i \(0.513307\pi\)
\(588\) −5.66959 −0.233810
\(589\) −30.4743 −1.25567
\(590\) −9.77782 −0.402547
\(591\) −10.6477 −0.437986
\(592\) −5.84241 −0.240121
\(593\) 8.40701 0.345234 0.172617 0.984989i \(-0.444778\pi\)
0.172617 + 0.984989i \(0.444778\pi\)
\(594\) 4.29127 0.176073
\(595\) 2.92592 0.119951
\(596\) 19.7775 0.810117
\(597\) 19.3870 0.793456
\(598\) −7.94401 −0.324855
\(599\) 20.3150 0.830049 0.415024 0.909810i \(-0.363773\pi\)
0.415024 + 0.909810i \(0.363773\pi\)
\(600\) 0.844163 0.0344628
\(601\) −1.00000 −0.0407909
\(602\) 5.02917 0.204974
\(603\) −26.4258 −1.07614
\(604\) −6.89037 −0.280365
\(605\) −10.0757 −0.409633
\(606\) 8.31673 0.337844
\(607\) −5.70283 −0.231471 −0.115735 0.993280i \(-0.536922\pi\)
−0.115735 + 0.993280i \(0.536922\pi\)
\(608\) −4.34072 −0.176039
\(609\) 3.29972 0.133711
\(610\) −5.61164 −0.227209
\(611\) 8.75949 0.354371
\(612\) 12.5637 0.507858
\(613\) −32.3291 −1.30576 −0.652880 0.757461i \(-0.726440\pi\)
−0.652880 + 0.757461i \(0.726440\pi\)
\(614\) 30.2322 1.22007
\(615\) 7.76744 0.313213
\(616\) 0.512155 0.0206353
\(617\) −32.7379 −1.31798 −0.658990 0.752152i \(-0.729016\pi\)
−0.658990 + 0.752152i \(0.729016\pi\)
\(618\) −12.9801 −0.522135
\(619\) 15.0430 0.604629 0.302315 0.953208i \(-0.402241\pi\)
0.302315 + 0.953208i \(0.402241\pi\)
\(620\) 7.02057 0.281953
\(621\) −29.4818 −1.18306
\(622\) 12.3450 0.494990
\(623\) 7.50942 0.300858
\(624\) −1.01527 −0.0406431
\(625\) 1.00000 0.0400000
\(626\) −31.9710 −1.27782
\(627\) 3.52294 0.140693
\(628\) −6.83852 −0.272887
\(629\) 32.0900 1.27951
\(630\) 1.21849 0.0485460
\(631\) −6.39353 −0.254522 −0.127261 0.991869i \(-0.540619\pi\)
−0.127261 + 0.991869i \(0.540619\pi\)
\(632\) −0.0908517 −0.00361389
\(633\) −17.2119 −0.684113
\(634\) −8.44300 −0.335314
\(635\) −5.62604 −0.223263
\(636\) 5.27134 0.209022
\(637\) 8.07753 0.320044
\(638\) 7.05481 0.279303
\(639\) 8.79919 0.348091
\(640\) 1.00000 0.0395285
\(641\) −0.779702 −0.0307964 −0.0153982 0.999881i \(-0.504902\pi\)
−0.0153982 + 0.999881i \(0.504902\pi\)
\(642\) −3.50930 −0.138501
\(643\) −4.27884 −0.168741 −0.0843705 0.996434i \(-0.526888\pi\)
−0.0843705 + 0.996434i \(0.526888\pi\)
\(644\) −3.51860 −0.138652
\(645\) −7.96965 −0.313805
\(646\) 23.8418 0.938045
\(647\) 19.4922 0.766316 0.383158 0.923683i \(-0.374836\pi\)
0.383158 + 0.923683i \(0.374836\pi\)
\(648\) 3.09431 0.121556
\(649\) 9.40069 0.369010
\(650\) −1.20269 −0.0471733
\(651\) −3.15706 −0.123735
\(652\) −2.76885 −0.108437
\(653\) −39.2685 −1.53669 −0.768347 0.640034i \(-0.778920\pi\)
−0.768347 + 0.640034i \(0.778920\pi\)
\(654\) −0.514526 −0.0201196
\(655\) 0.518832 0.0202725
\(656\) 9.20135 0.359252
\(657\) −17.2548 −0.673172
\(658\) 3.87980 0.151250
\(659\) 27.5689 1.07393 0.536966 0.843604i \(-0.319570\pi\)
0.536966 + 0.843604i \(0.319570\pi\)
\(660\) −0.811604 −0.0315916
\(661\) 10.0809 0.392101 0.196050 0.980594i \(-0.437188\pi\)
0.196050 + 0.980594i \(0.437188\pi\)
\(662\) 16.6072 0.645458
\(663\) 5.57645 0.216571
\(664\) −13.2425 −0.513908
\(665\) 2.31231 0.0896673
\(666\) 13.3639 0.517839
\(667\) −48.4679 −1.87668
\(668\) −4.26084 −0.164857
\(669\) −15.4363 −0.596802
\(670\) 11.5528 0.446324
\(671\) 5.39520 0.208280
\(672\) −0.449687 −0.0173470
\(673\) −20.8497 −0.803698 −0.401849 0.915706i \(-0.631632\pi\)
−0.401849 + 0.915706i \(0.631632\pi\)
\(674\) −14.1086 −0.543442
\(675\) −4.46342 −0.171797
\(676\) −11.5535 −0.444367
\(677\) 32.6106 1.25333 0.626664 0.779290i \(-0.284420\pi\)
0.626664 + 0.779290i \(0.284420\pi\)
\(678\) −4.52939 −0.173950
\(679\) −4.44940 −0.170752
\(680\) −5.49260 −0.210632
\(681\) 20.2077 0.774360
\(682\) −6.74979 −0.258463
\(683\) −37.6401 −1.44026 −0.720129 0.693840i \(-0.755917\pi\)
−0.720129 + 0.693840i \(0.755917\pi\)
\(684\) 9.92891 0.379641
\(685\) −4.41924 −0.168850
\(686\) 7.30665 0.278969
\(687\) 19.5060 0.744200
\(688\) −9.44089 −0.359931
\(689\) −7.51014 −0.286113
\(690\) 5.57587 0.212270
\(691\) −43.6848 −1.66185 −0.830923 0.556387i \(-0.812187\pi\)
−0.830923 + 0.556387i \(0.812187\pi\)
\(692\) 8.79251 0.334241
\(693\) −1.17150 −0.0445015
\(694\) −33.9642 −1.28926
\(695\) −22.4968 −0.853352
\(696\) −6.19432 −0.234795
\(697\) −50.5393 −1.91431
\(698\) 13.0855 0.495295
\(699\) 8.90555 0.336839
\(700\) −0.532701 −0.0201342
\(701\) −46.4998 −1.75627 −0.878137 0.478410i \(-0.841213\pi\)
−0.878137 + 0.478410i \(0.841213\pi\)
\(702\) 5.36810 0.202606
\(703\) 25.3602 0.956480
\(704\) −0.961430 −0.0362353
\(705\) −6.14825 −0.231557
\(706\) −16.0428 −0.603779
\(707\) −5.24820 −0.197379
\(708\) −8.25407 −0.310207
\(709\) 31.5037 1.18315 0.591574 0.806251i \(-0.298507\pi\)
0.591574 + 0.806251i \(0.298507\pi\)
\(710\) −3.84683 −0.144369
\(711\) 0.207813 0.00779360
\(712\) −14.0969 −0.528302
\(713\) 46.3723 1.73666
\(714\) 2.46995 0.0924355
\(715\) 1.15630 0.0432432
\(716\) 11.7877 0.440525
\(717\) 2.51225 0.0938217
\(718\) 0.802407 0.0299455
\(719\) −40.2451 −1.50089 −0.750444 0.660934i \(-0.770160\pi\)
−0.750444 + 0.660934i \(0.770160\pi\)
\(720\) −2.28739 −0.0852459
\(721\) 8.19096 0.305047
\(722\) −0.158171 −0.00588651
\(723\) −18.7820 −0.698510
\(724\) 24.3416 0.904648
\(725\) −7.33783 −0.272520
\(726\) −8.50549 −0.315668
\(727\) 29.2020 1.08304 0.541522 0.840687i \(-0.317848\pi\)
0.541522 + 0.840687i \(0.317848\pi\)
\(728\) 0.640674 0.0237449
\(729\) 4.22566 0.156506
\(730\) 7.54343 0.279195
\(731\) 51.8551 1.91793
\(732\) −4.73714 −0.175090
\(733\) −42.4811 −1.56908 −0.784538 0.620080i \(-0.787100\pi\)
−0.784538 + 0.620080i \(0.787100\pi\)
\(734\) 7.01696 0.259001
\(735\) −5.66959 −0.209126
\(736\) 6.60521 0.243471
\(737\) −11.1072 −0.409140
\(738\) −21.0471 −0.774753
\(739\) 11.0192 0.405346 0.202673 0.979246i \(-0.435037\pi\)
0.202673 + 0.979246i \(0.435037\pi\)
\(740\) −5.84241 −0.214771
\(741\) 4.40698 0.161894
\(742\) −3.32643 −0.122117
\(743\) 35.5120 1.30281 0.651404 0.758731i \(-0.274180\pi\)
0.651404 + 0.758731i \(0.274180\pi\)
\(744\) 5.92651 0.217276
\(745\) 19.7775 0.724591
\(746\) 14.4241 0.528106
\(747\) 30.2907 1.10828
\(748\) 5.28076 0.193084
\(749\) 2.21451 0.0809165
\(750\) 0.844163 0.0308245
\(751\) −44.2767 −1.61568 −0.807840 0.589402i \(-0.799364\pi\)
−0.807840 + 0.589402i \(0.799364\pi\)
\(752\) −7.28325 −0.265593
\(753\) −10.4677 −0.381465
\(754\) 8.82512 0.321392
\(755\) −6.89037 −0.250766
\(756\) 2.37767 0.0864749
\(757\) 17.9051 0.650771 0.325386 0.945581i \(-0.394506\pi\)
0.325386 + 0.945581i \(0.394506\pi\)
\(758\) −0.642511 −0.0233371
\(759\) −5.36081 −0.194585
\(760\) −4.34072 −0.157454
\(761\) −6.96672 −0.252543 −0.126272 0.991996i \(-0.540301\pi\)
−0.126272 + 0.991996i \(0.540301\pi\)
\(762\) −4.74930 −0.172049
\(763\) 0.324687 0.0117544
\(764\) 12.8086 0.463398
\(765\) 12.5637 0.454242
\(766\) −8.96481 −0.323912
\(767\) 11.7597 0.424617
\(768\) 0.844163 0.0304611
\(769\) −22.6634 −0.817265 −0.408632 0.912699i \(-0.633994\pi\)
−0.408632 + 0.912699i \(0.633994\pi\)
\(770\) 0.512155 0.0184568
\(771\) −1.75565 −0.0632284
\(772\) 20.6520 0.743283
\(773\) 40.9769 1.47384 0.736918 0.675982i \(-0.236280\pi\)
0.736918 + 0.675982i \(0.236280\pi\)
\(774\) 21.5950 0.776216
\(775\) 7.02057 0.252186
\(776\) 8.35252 0.299838
\(777\) 2.62725 0.0942521
\(778\) 37.1210 1.33085
\(779\) −39.9404 −1.43101
\(780\) −1.01527 −0.0363523
\(781\) 3.69846 0.132341
\(782\) −36.2798 −1.29736
\(783\) 32.7518 1.17045
\(784\) −6.71623 −0.239865
\(785\) −6.83852 −0.244077
\(786\) 0.437979 0.0156222
\(787\) 0.254953 0.00908809 0.00454404 0.999990i \(-0.498554\pi\)
0.00454404 + 0.999990i \(0.498554\pi\)
\(788\) −12.6133 −0.449329
\(789\) 4.21208 0.149954
\(790\) −0.0908517 −0.00323236
\(791\) 2.85823 0.101627
\(792\) 2.19917 0.0781439
\(793\) 6.74906 0.239666
\(794\) −19.5965 −0.695455
\(795\) 5.27134 0.186955
\(796\) 22.9659 0.814005
\(797\) 30.3945 1.07663 0.538313 0.842745i \(-0.319062\pi\)
0.538313 + 0.842745i \(0.319062\pi\)
\(798\) 1.95196 0.0690987
\(799\) 40.0040 1.41524
\(800\) 1.00000 0.0353553
\(801\) 32.2450 1.13932
\(802\) −15.5264 −0.548256
\(803\) −7.25248 −0.255934
\(804\) 9.75245 0.343942
\(805\) −3.51860 −0.124014
\(806\) −8.44357 −0.297412
\(807\) 0.766713 0.0269896
\(808\) 9.85205 0.346594
\(809\) −54.6837 −1.92258 −0.961289 0.275543i \(-0.911142\pi\)
−0.961289 + 0.275543i \(0.911142\pi\)
\(810\) 3.09431 0.108723
\(811\) −25.5682 −0.897819 −0.448910 0.893577i \(-0.648188\pi\)
−0.448910 + 0.893577i \(0.648188\pi\)
\(812\) 3.90887 0.137174
\(813\) 14.0802 0.493814
\(814\) 5.61707 0.196878
\(815\) −2.76885 −0.0969886
\(816\) −4.63665 −0.162315
\(817\) 40.9802 1.43372
\(818\) −24.6582 −0.862155
\(819\) −1.46547 −0.0512077
\(820\) 9.20135 0.321325
\(821\) −19.6687 −0.686441 −0.343221 0.939255i \(-0.611518\pi\)
−0.343221 + 0.939255i \(0.611518\pi\)
\(822\) −3.73056 −0.130118
\(823\) −1.93117 −0.0673163 −0.0336582 0.999433i \(-0.510716\pi\)
−0.0336582 + 0.999433i \(0.510716\pi\)
\(824\) −15.3763 −0.535658
\(825\) −0.811604 −0.0282564
\(826\) 5.20866 0.181232
\(827\) −40.2192 −1.39856 −0.699280 0.714848i \(-0.746496\pi\)
−0.699280 + 0.714848i \(0.746496\pi\)
\(828\) −15.1087 −0.525063
\(829\) 20.8718 0.724907 0.362454 0.932002i \(-0.381939\pi\)
0.362454 + 0.932002i \(0.381939\pi\)
\(830\) −13.2425 −0.459653
\(831\) 22.9147 0.794903
\(832\) −1.20269 −0.0416957
\(833\) 36.8896 1.27815
\(834\) −18.9910 −0.657603
\(835\) −4.26084 −0.147453
\(836\) 4.17330 0.144337
\(837\) −31.3358 −1.08312
\(838\) −17.9818 −0.621172
\(839\) −13.1018 −0.452325 −0.226162 0.974090i \(-0.572618\pi\)
−0.226162 + 0.974090i \(0.572618\pi\)
\(840\) −0.449687 −0.0155157
\(841\) 24.8437 0.856679
\(842\) 0.752344 0.0259275
\(843\) −13.2535 −0.456476
\(844\) −20.3893 −0.701830
\(845\) −11.5535 −0.397454
\(846\) 16.6596 0.572770
\(847\) 5.36731 0.184423
\(848\) 6.24445 0.214435
\(849\) 14.7964 0.507810
\(850\) −5.49260 −0.188395
\(851\) −38.5903 −1.32286
\(852\) −3.24735 −0.111252
\(853\) 10.5851 0.362426 0.181213 0.983444i \(-0.441998\pi\)
0.181213 + 0.983444i \(0.441998\pi\)
\(854\) 2.98933 0.102293
\(855\) 9.92891 0.339562
\(856\) −4.15714 −0.142088
\(857\) −49.1792 −1.67993 −0.839964 0.542642i \(-0.817424\pi\)
−0.839964 + 0.542642i \(0.817424\pi\)
\(858\) 0.976107 0.0333237
\(859\) −6.37161 −0.217397 −0.108698 0.994075i \(-0.534668\pi\)
−0.108698 + 0.994075i \(0.534668\pi\)
\(860\) −9.44089 −0.321932
\(861\) −4.13772 −0.141013
\(862\) 20.3211 0.692139
\(863\) 27.6061 0.939723 0.469861 0.882740i \(-0.344304\pi\)
0.469861 + 0.882740i \(0.344304\pi\)
\(864\) −4.46342 −0.151849
\(865\) 8.79251 0.298954
\(866\) −33.7894 −1.14821
\(867\) 11.1165 0.377537
\(868\) −3.73987 −0.126939
\(869\) 0.0873476 0.00296306
\(870\) −6.19432 −0.210007
\(871\) −13.8944 −0.470795
\(872\) −0.609510 −0.0206406
\(873\) −19.1055 −0.646622
\(874\) −28.6713 −0.969823
\(875\) −0.532701 −0.0180086
\(876\) 6.36788 0.215151
\(877\) 14.0886 0.475737 0.237869 0.971297i \(-0.423551\pi\)
0.237869 + 0.971297i \(0.423551\pi\)
\(878\) −22.3552 −0.754451
\(879\) −23.4478 −0.790873
\(880\) −0.961430 −0.0324098
\(881\) 24.2259 0.816190 0.408095 0.912939i \(-0.366193\pi\)
0.408095 + 0.912939i \(0.366193\pi\)
\(882\) 15.3626 0.517287
\(883\) 37.8604 1.27410 0.637052 0.770821i \(-0.280154\pi\)
0.637052 + 0.770821i \(0.280154\pi\)
\(884\) 6.60589 0.222180
\(885\) −8.25407 −0.277458
\(886\) 21.2089 0.712526
\(887\) −40.0641 −1.34522 −0.672611 0.739996i \(-0.734827\pi\)
−0.672611 + 0.739996i \(0.734827\pi\)
\(888\) −4.93194 −0.165505
\(889\) 2.99700 0.100516
\(890\) −14.0969 −0.472528
\(891\) −2.97497 −0.0996652
\(892\) −18.2859 −0.612258
\(893\) 31.6145 1.05794
\(894\) 16.6954 0.558378
\(895\) 11.7877 0.394018
\(896\) −0.532701 −0.0177963
\(897\) −6.70604 −0.223908
\(898\) −24.8674 −0.829835
\(899\) −51.5157 −1.71815
\(900\) −2.28739 −0.0762463
\(901\) −34.2983 −1.14264
\(902\) −8.84645 −0.294555
\(903\) 4.24544 0.141279
\(904\) −5.36554 −0.178455
\(905\) 24.3416 0.809142
\(906\) −5.81659 −0.193243
\(907\) 47.2600 1.56924 0.784621 0.619975i \(-0.212857\pi\)
0.784621 + 0.619975i \(0.212857\pi\)
\(908\) 23.9381 0.794414
\(909\) −22.5355 −0.747454
\(910\) 0.640674 0.0212381
\(911\) 10.6548 0.353008 0.176504 0.984300i \(-0.443521\pi\)
0.176504 + 0.984300i \(0.443521\pi\)
\(912\) −3.66427 −0.121336
\(913\) 12.7317 0.421358
\(914\) 38.5370 1.27469
\(915\) −4.73714 −0.156605
\(916\) 23.1069 0.763473
\(917\) −0.276383 −0.00912696
\(918\) 24.5158 0.809141
\(919\) −4.25145 −0.140242 −0.0701212 0.997538i \(-0.522339\pi\)
−0.0701212 + 0.997538i \(0.522339\pi\)
\(920\) 6.60521 0.217767
\(921\) 25.5209 0.840944
\(922\) 14.0184 0.461672
\(923\) 4.62654 0.152284
\(924\) 0.432342 0.0142230
\(925\) −5.84241 −0.192097
\(926\) 33.7519 1.10915
\(927\) 35.1715 1.15518
\(928\) −7.33783 −0.240876
\(929\) 44.4081 1.45698 0.728492 0.685055i \(-0.240222\pi\)
0.728492 + 0.685055i \(0.240222\pi\)
\(930\) 5.92651 0.194338
\(931\) 29.1533 0.955459
\(932\) 10.5496 0.345562
\(933\) 10.4212 0.341175
\(934\) 37.4995 1.22702
\(935\) 5.28076 0.172699
\(936\) 2.75102 0.0899198
\(937\) 5.47272 0.178786 0.0893930 0.995996i \(-0.471507\pi\)
0.0893930 + 0.995996i \(0.471507\pi\)
\(938\) −6.15419 −0.200942
\(939\) −26.9887 −0.880744
\(940\) −7.28325 −0.237554
\(941\) −50.5208 −1.64693 −0.823466 0.567366i \(-0.807963\pi\)
−0.823466 + 0.567366i \(0.807963\pi\)
\(942\) −5.77283 −0.188089
\(943\) 60.7768 1.97916
\(944\) −9.77782 −0.318241
\(945\) 2.37767 0.0773455
\(946\) 9.07676 0.295111
\(947\) 32.7854 1.06538 0.532691 0.846310i \(-0.321181\pi\)
0.532691 + 0.846310i \(0.321181\pi\)
\(948\) −0.0766937 −0.00249089
\(949\) −9.07240 −0.294502
\(950\) −4.34072 −0.140831
\(951\) −7.12726 −0.231117
\(952\) 2.92592 0.0948295
\(953\) −13.6612 −0.442528 −0.221264 0.975214i \(-0.571018\pi\)
−0.221264 + 0.975214i \(0.571018\pi\)
\(954\) −14.2835 −0.462445
\(955\) 12.8086 0.414476
\(956\) 2.97603 0.0962515
\(957\) 5.95541 0.192511
\(958\) −31.2817 −1.01066
\(959\) 2.35413 0.0760189
\(960\) 0.844163 0.0272452
\(961\) 18.2884 0.589950
\(962\) 7.02660 0.226547
\(963\) 9.50899 0.306423
\(964\) −22.2492 −0.716600
\(965\) 20.6520 0.664812
\(966\) −2.97027 −0.0955670
\(967\) −8.52830 −0.274252 −0.137126 0.990554i \(-0.543786\pi\)
−0.137126 + 0.990554i \(0.543786\pi\)
\(968\) −10.0757 −0.323844
\(969\) 20.1264 0.646553
\(970\) 8.35252 0.268183
\(971\) −19.4931 −0.625562 −0.312781 0.949825i \(-0.601261\pi\)
−0.312781 + 0.949825i \(0.601261\pi\)
\(972\) 16.0024 0.513276
\(973\) 11.9841 0.384191
\(974\) 9.32490 0.298789
\(975\) −1.01527 −0.0325145
\(976\) −5.61164 −0.179624
\(977\) −14.6151 −0.467578 −0.233789 0.972287i \(-0.575112\pi\)
−0.233789 + 0.972287i \(0.575112\pi\)
\(978\) −2.33736 −0.0747405
\(979\) 13.5532 0.433161
\(980\) −6.71623 −0.214542
\(981\) 1.39419 0.0445129
\(982\) 34.9844 1.11640
\(983\) 33.2877 1.06171 0.530856 0.847462i \(-0.321871\pi\)
0.530856 + 0.847462i \(0.321871\pi\)
\(984\) 7.76744 0.247617
\(985\) −12.6133 −0.401892
\(986\) 40.3038 1.28353
\(987\) 3.27518 0.104250
\(988\) 5.22053 0.166087
\(989\) −62.3590 −1.98290
\(990\) 2.19917 0.0698941
\(991\) 37.9919 1.20685 0.603426 0.797419i \(-0.293802\pi\)
0.603426 + 0.797419i \(0.293802\pi\)
\(992\) 7.02057 0.222903
\(993\) 14.0192 0.444886
\(994\) 2.04921 0.0649970
\(995\) 22.9659 0.728068
\(996\) −11.1788 −0.354214
\(997\) −47.0677 −1.49065 −0.745325 0.666701i \(-0.767706\pi\)
−0.745325 + 0.666701i \(0.767706\pi\)
\(998\) −37.5728 −1.18935
\(999\) 26.0771 0.825043
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))